[FOM] Falsify Platonism?

Lucas Kruijswijk L.B.Kruijswijk at inter.nl.net
Thu Apr 29 18:39:33 EDT 2010

Dear all,

I started this thread with a rather innocent remark at
the end of question. I would like to make a few remarkts.

First of all, with 'falsify' I referred to science philosopher
Karl Popper. The idea is that if there is no potential that
a scientific theory can be falsified, you may question
whether the theory means something. With this one can
criticize the theory of the 'existence of God', since the
followers of that theory do not give a way to falsify
that theory.

I noticed, that in Hilbert's program does follow the
principles of Karl Popper, since the questions he stated
could lead to a negative result. Unfortunately most the
questions lead to a negative result. Yet, this can be
marked as proper science.

I noticed that for the philosophy of Platonism I can
not find an argument in the articles I found on internet
that fits the criteria of Karl Popper.

In this discussion it has been said that if PA is
inconsistent, it would falsify Platonism. Although, this
can be considered true, it is not satisfactory for two
- It is rather unlikely that PA is inconsistent. So, it is 
  a rather easy way to show the correctness of the
  existence of God, uhhh, I mean of Platonism.
- Second, if PA is inconsistent, than many other philosophies
  about the foundation of mathematics have a problem. So, it
  is not a discriminating factor between philosophies
  (although Brouwer didn't like formalizing at all, so, then he
  might be right).

Considering the fact that the group of experts on FOM, could
not agree what could potentially falsify Platonism, I conclude,
based on the philosophy of Karl Popper, that Platonism does
not have much meaning.

Although, I do have a private idea.

If it turns out that in the formalizations of mathematics, the
entity (human or computer) that performs the mathematics,
can not be fully separated from the mathematics it performs,
then Platonism is falsified, since Platonism assumes a 
mathematical world, independent from the entities that are
using it.

Or in other words, if thinking about ourselves is crucial
for mathematics, then Platonism is falsified.



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